Planar graphs with maximum degree 4 are strongly 19-edge-colorable

A strong edge-coloring of a graph is a proper edge-coloring such that edges at distance at most 2 receive different colors. It is known that every planar graph has a strong edge-coloring by using at most $4\Delta +4$ colors, where $\Delta$ denotes the maximum degree of the graph. In this paper, we will show that 19 colors are enough to color a planar graph with maximum degree 4.     

股票价格随机变动的内生性解释及其应用

建立了一个非对称信息下的重复博弈模型来刻画股票市场中庄家和散户的博弈行为,推导出股票价格的折现过程服从一个由布朗运动驱动的鞅过程,并给出股票价格随机变动的内生性解释:在博弈过程中庄家为了隐藏散户所不知道的信息采用随机化策略来迷惑对手,从而导致股票价格的随机变动.在此基础上,进一步研究了相应的期权定价问题并给出期权定价公式.     

On the Laplacian, signless Laplacian and normalized Laplacian characteristic polynomials of a graph

The Laplacian, signless Laplacian and normalized Laplacian characteristic polynomials of a graph are the characteristic polynomials of its Laplacian matrix, signless Laplacian matrix and normalized Laplacian matrix, respectively. In this paper, we mainly derive six reduction procedures on the Laplacian, signless Laplacian and normalized Laplacian characteristic polynomials of a graph which can be used to construct larger Laplacian, signless Laplacian and normalized Laplacian cospectral graphs, respectively.     

On the second largest Laplacian eigenvalues of graphs

The second largest Laplacian eigenvalue of a graph is the second largest eigenvalue of the associated Laplacian matrix. In this paper, we study extremal graphs for the extremal values of the second largest Laplacian eigenvalue and the Laplacian separator of a connected graph, respectively. All simple connected graphs with second largest Laplacian eigenvalue at most 3 are characterized. It is also shown that graphs with second largest Laplacian eigenvalue at most 3 are determined by their Laplacian spectrum. Moreover, the graphs with maximum and the second maximum Laplacian separators among all connected graphs are determined.     

Improving artificial bee colony with one-position inheritance mechanism

Artificial bee colony (ABC) algorithm simulates the foraging behavior of honey bees. It shows good performance in many application problems and large scale optimization problems. However, variation of a solution in the ABC algorithm is only employed on one dimension of the solution. This would sometimes hamper the convergence speed of the ABC algorithm, especially for large scale optimization. This paper proposes a one-position inheritance (OPI) mechanism to overcome this drawback. The OPI mechanism aims to promote information exchange amongst employed bees of the ABC algorithm. For separable function, OPIABC has a higher probability resulting in function value improvement of the worst positions than ABC. Through one-position information exchange, the OPI mechanism can assist the ABC algorithm to find promising solutions. This mechanism has been tested on a set of 25 test functions with $D= 30$ and on CEC 2008 test suite with $D= 100$ and 1,000. Experimental results show that the OPI mechanism can speed up the convergence of the ABC algorithm. After the use of OPI, the performance of the ABC algorithm is significantly improved for both rotated problems and large scale problems. OPIABC is also competitive on both test suites comparing with other recently proposed swarm intelligence metaheuristics (e.g. SaDE and PSO2011). Furthermore, the OPI mechanism can greatly enhance the performance of other improved ABC algorithms.     

L（j,k）-number of Direct Product of Path and Cycle

For positive numbers j and k, an L(j,k)-labeling f of G is an assignment of numbers to vertices of G such that |f(u)-f(v)|≥j if uv∈E(G), and |f(u)-f(v)|≥k if d(u,v)=2. Then the span of f is the difference between the maximum and the minimum numbers assigned by f. The L(j,k)-number of G, denoted by λj,k(G), is the minimum span over all L(j,k)-labelings of G. In this paper, we give some results about the L(j,k)-number of the direct product of a path and a cycle for j≤k.     

Interfacial Enhancement by γ‐Al2O3 of Electrochemical Oxidative Dehydrogenation of Ethane to Ethylene in Solid Oxide Electrolysis Cells

Oxidative dehydrogenation of ethane (ODE) is limited by the facile deep oxidation and potential safety hazards. Now, electrochemical ODE reaction is incorporated into the anode of a solid oxide electrolysis cell, utilizing the oxygen species generated at anode to catalytically convert ethane. By infiltrating γ‐Al₂O₃ onto the surface of La_0.6Sr_0.4Co_0.2Fe_0.8O_3‐δ‐Sm_0.2Ce_0.8O_2‐δ (LSCF‐SDC) anode, the ethylene selectivity reaches as high as 92.5 %, while the highest ethane conversion is up to 29.1 % at 600 °C with optimized current and ethane flow rate. Density functional theory calculations and in situ X‐ray photoelectron spectroscopy characterizations reveal that the Al₂O₃/LSCF interfaces effectively reduce the amount of adsorbed oxygen species, leading to improved ethylene selectivity and stability, and that the formation of Al‐O‐Fe alters the electronic structure of interfacial Fe center with increased density of state around Fermi level and downshift of the empty band, which enhances ethane adsorption and conversion.     

Cu(I)-catalyzed asymmetric diamination of conjugated dienes

A Cu(I)-catalyzed asymmetric diamination for a variety of conjugated dienes and a triene with encouraging ee's has been effectively achieved using (R)-DTBM-SEGPHOS as a chiral ligand and di- tert-butyldiaziridinone as the nitrogen source.     

Cyclic bandwidth with an edge added

B_c(G) denotes the cyclic bandwidth of graph G. In this paper, we obtain the maximum cyclic bandwidth of graphs of order p with adding an edge as follows:

     

Syntheses and Structural Characterization of 1D Coordination Polymers of Transition‐Metal Atoms Containing 2,4‐Pyridinedicarboxylate Bridges

By employing one bridging ligand, 2,4‐pyridinedicarboxylate (2,4‐pda^2?), three one‐dimensional (1D) coordination polymers of [Cu(2,4‐pda)(H₂O)₂]_∞ ( 1 ), {[Cu₄(2,4‐pda)₄(H₂O)₈]·3H₂O}_∞ ( 2 ), and {[Cd(2,4‐pda)(H₂O)₃]·H₂O}_∞ ( 3 ) were synthesized. A simple zigzag polymeric chain is observed for both 1 and 3 , but a railroad‐like zigzag polymeric chain is observed for 2. Almost all water molecules, whether coordinated or not, are involved in hydrogen bonding interactions and help to tie up the 1D polymeric chains of 1‐3 into a three‐dimensional (3D) network. A comparison about the coordination geometries in all similar coordination polymers available to date is also included.